Which of the equations are true identities? A. (9k-8)(9k+8)=81k^(2)+64 B. (3m+2n)(6m-4n)=18m^(2)-8n^(2) Choose 1 answer: (A) Only A (B) Only B (C) Both A and B (D) Neither A nor B

Expand A using formula: Let's expand A: (9k-8)(9k+8) using the difference of squares formula, which is (a-b)(a+b)=a^2-b^2.Check B using FOIL method: So, (9k-8)(9k+8) = (9k)^2 - (8)^2 = 81k^2 - 64.Simplify B using FOIL: Now let's check B: (3m+2n)(6m-4n) using the FOIL method, which stands for First, Outer, Inner, Last.Compare expansions to given equations: So, (3m+2n)(6m-4n) = 3m*6m + 3m*(-4n) + 2n*6m + 2n*(-4n).Verify A as true identity: That simplifies to 18m^2 - 12mn + 12mn - 8n^2.Verify B as true identity: The middle terms, -12mn and +12mn, cancel each other out, so we're left with 18m^2 - 8n^2.Final answer: Now we compare our expansions to the given equations.For A, we got 81k^2 - 64, which matches the given equation, so A is a true identity.For B, we got 18m^2 - 8n^2, which also matches the given equation, so B is a true identity too.Since both A and B are true identities, the correct answer is (C) Both A and B.

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Which of the equations are true identities?
A.
(9k-8)(9k+8)=81k^(2)+64
B.
(3m+2n)(6m-4n)=18m^(2)-8n^(2)
Choose 1 answer:
(A) Only A
(B) Only B
(C) Both A and B
(D) Neither
A nor
B

Which of the equations are true identities? $\newline$ A. $(9 k-8)(9 k+8)=81 k^{2}+64$ $\newline$ B. $(3 m+2 n)(6 m-4 n)=18 m^{2}-8 n^{2}$ $\newline$ Choose $1$ answer: $\newline$ (A) Only A $\newline$ (B) Only B $\newline$ (C) Both A and B $\newline$ (D) Neither $\mathrm{A}$ nor $\mathrm{B}$

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Calculus

Find derivatives of using multiple formulae

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Q. Which of the equations are true identities?

\newline

(9 k-8)(9 k+8)=81 k^{2}+64

\newline

(3 m+2 n)(6 m-4 n)=18 m^{2}-8 n^{2}

\newline

Choose

1

answer:

\newline

(A) Only A

\newline

(B) Only B

\newline

\newline

(D) Neither

\mathrm{A}

nor

\mathrm{B}

Expand A using formula: Let's expand $A$ : $(9k-8)(9k+8)$ using the difference of squares formula, which is $(a-b)(a+b)=a^2-b^2$ .
Check B using FOIL method: So, $(9k-8)(9k+8) = (9k)^2 - (8)^2 = 81k^2 - 64$ .
Simplify B using FOIL: Now let's check B: \(3m+ $2$ n)( $6$ m $-4$ n)\ using the FOIL method, which stands for First, Outer, Inner, Last.
Compare expansions to given equations: So, $(3m+2n)(6m-4n) = 3m\cdot 6m + 3m\cdot (-4n) + 2n\cdot 6m + 2n\cdot (-4n)$ .
Verify $A$ as true identity: That simplifies to $18m^2 - 12mn + 12mn - 8n^2$ .
Verify B as true identity: The middle terms, $-12mn$ and $+12mn$ , cancel each other out, so we're left with $18m^2 - 8n^2$ .
Final answer: Now we compare our expansions to the given equations.
Final answer: Now we compare our expansions to the given equations.For A, we got $81k^2 - 64$ , which matches the given equation, so A is a true identity.
Final answer: Now we compare our expansions to the given equations. For $A$ , we got $81k^2 - 64$ , which matches the given equation, so $A$ is a true identity. For $B$ , we got $18m^2 - 8n^2$ , which also matches the given equation, so $B$ is a true identity too.
Final answer: Now we compare our expansions to the given equations. For $A$ , we got $81k^2 - 64$ , which matches the given equation, so $A$ is a true identity. For $B$ , we got $18m^2 - 8n^2$ , which also matches the given equation, so $B$ is a true identity too. Since both $A$ and $B$ are true identities, the correct answer is $(C)$ Both $A$ and $B$ .